INTERMEDIATE ALGEBRA Review for Exam 3

Transcription

1 INTERMEDIATE ALGEBRA Review for Eam 3 Consider the polnomials below. Answer the questions. 1) a) b) u + 9u9v2 + u4v3 + 7u + 4v6 i) Determine the degree of each term of the polnomial. ii) Determine the degree of the polnomial. iii) Find the leading term. iv) Find the leading coefficient. Find the function value. 2) a) Find P(-2): P() = b) Find P(- 1 ): P() = Solve the problem. 3) The position of an object moving in a straight line is given b s = 4t2-3t, where s is in meters and t is the time in seconds the object has been in motion. How far will an object move in 7 seconds? 4) A() = gives the alcohol level in an average person's bloodstream hours after drinking 8 oz of 0-proof whiske. If the level eceeds 1. units, a person is legall drunk. Would a person be drunk after 4 hours? Perform the indicated operation and simplif, if possible. ) a) (8 + 9n6-8n) + (8n6-3n + 3) b) ( ) + ( ) c) (2r2s2 + 3r2s - 7rs) + (7r2s2-2r2s + 7rs - 4) 6) a) (-4n + n + n2) - (-1n2 + 7n - 11n) b) ( ) - ( ) Multipl. 7) a) -72 œ 63 b) 82( ) c) d) (2p - 1)(4p2 + 2p + 1) 8) a) Let P() = 7-9 and Q() = Find P() œ Q(). b) Let Q() = Find [Q()]2 9) a) (w - 6)2 b) (7 + 9)2 c) (32-3) 2 ) a) (11r - )(11r + ) b) (32 + )(32 - ) c) ( )( ) d) ( + + 9)( + - 9) 11) a) (4 + 7)( + 8) b) ( - 2)( - 3) c) (3 + )( - 11) d) (2 + 7)(3 - ) Factor. 12) a) 32m9 + 40m6-36m4 b) Factor out a factor with a negative coefficient. 13) a) -2u4 + 1u3 - u b) -j3-6j2 + j - 13 Factor. 14) ) 6a3 + 8a2b + 1ab2 + 20b3 16)

2 MATD 0390 Eam 3 Review Page 2 17) u2 - uv - 14v2 18) -m2 + 3m ) ) ) ) 24a2-20a ) ) ) ) 2p2-70p ) ) ) 81k2-0m2 30) ) (q - 6) ) 98-9z8 33) mn 2-9m - 7n ) ) ) 8a3-12b3 37) 12s ) p6-64z6 Solve the equation. 39) (2 + 4) = 42 40) = 0 41) 2 - = 72 42) 30d2 + 48d + 18 = 0 43) 49k2-2 = 0 44) 12n2 + 18n = 0 4) ( + )( + 9) = 32 Solve the problem. 46) If f() = 2-6 and g() = 20-24, find all -values for which f() = g(). Solve. 47) A triangular garden has an area of 168 square feet. The height is feet more than the base. Find the base of the garden. 48) A lot is in the shape of a right triangle. The shorter leg measures 60 meters. The hpotenuse is 20 meters longer than the length of the longer leg. How long is the longer leg? 49) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 1 feet. Find the length of the ladder if the length is feet more than its distance from the wall. Find the function value, provided it eists. 0) a) f() = ; f(-3) 8 b) f() = ; f(-4) Write in simplified form and list all restrictions on the domain. 7-1) f() = ) f() = 2 + 7

3 MATD 0390 Eam 3 Review Page 3 3) f() = Multipl and simplif. 4) 2p - 2 p2 œ p 9p - 9 ) œ ) k 2 + k + 2 k2 + 14k + 4 œ Divide and simplif ) d ) d ) z2 + z + 6 z2 + 11z + 24 d Graph. 60) f() = ) f() = ) + 2 = 0 63) -7 - = 0 k2 + 9k k2-2k - 3 z2 + 2z z2 + 6z - 16 Find the - and -intercepts for the equation. Then graph the equation. 64) 8-2 = - 6) 4-8 f() = 16 67) If ou rent a car for one da and drive 20 miles, the cost is $2. If ou drive 400 miles, the cost is $147. a) Find a linear function that epresses the cost C, in dollars, as a function of the number of miles driven, m. b) Use this function to find the cost if ou rent the car for one da and drive it 0 miles. 68) A gas station sells 4820 gallons of regular unleaded gasoline on a da when the charge $1.3 per gallon, whereas the sell 397 gallons on a da that the charge $1.40 per gallon. Let f() represent the number of gallons sold as a function of price,. Find a linear function that fits the data. 69) A freight train leaves a station traveling at 40 mph. Eight hours later, a passenger train leaves the same station traveling in the same direction at 60 mph. How long does it take for the passenger train to catch up to the freight train? How far have the travelled when this happens? 70) There were 39,000 people at a ball game in Los Angeles. The da's receipts were $ 28,000. How man people paid $12.00 for reserved seats and how man paid $.00 for general admission? 71) In a chemistr class, a 4% silver iodide solution must be mied with a % silver iodide solution to get. liters of a 6% solution. How man liters of each solution are needed? Solve the problem. 66) A ta-eempt school group received a bill of $ for educational software. The bill incorrectl included sales ta of 7%. How much should the school group pa?

4 Answer Ke Testname: IAREVIEW3SU06 1) a) i) -163: degree 3; 6: degree 1; 34: degree 4; -2: degree 0; -8: degree 2 ii) degree 4 iii) 34 iv) 3 b) i) u: degree ; 9u9v2: degree 11; u4v3: degee 7; 7u: degree 1; 4v6: degree 6 ii) degree 11 iii) 9u9v2 iv) 9 2) a) 1 b) ) 17 meters 4) Yes ) a) 17n6-11n + 11 b) c) 9r2s2 + r2s - 4 6) a) -2n + 20n2 + 7n b) ) a) -42 b) c) d) 8p3-1 8) a) b) ) a) w2-12w + 36 b) c) ) a) 121r2-2 b) 94-2 c) d) ) a) b) c) d) ) a) 4m4(8m + m2-9) b) 1243( ) 13) a) -u(u3-3u2 + 2) b) -(j3 + 6j2 - j + 13) 14) ( + 2)(3-4) 1) (2a2 + b2)(3a + 4b) 16) ( + 6)( - 7) 17) (u + 2v)(u - 7v) 18) (7 - m)(m + 4) or (m - 7)(-m - 4) 19) Prime 20) (3 + 4)(4 + 3) 21) (3 + 1)(3-4) 22) 4(3a - 1)(2a - 1) 23) 8(2-1)( + ) 24) 3( + 8)( - 2) 2) ( + 12)2 26) (p - 7)2 27) (4 + ) 2 28) (8 + 3)(8-3) 29) (9k + m)(9k - m) 30) 3( - 3)( + 3) 31) (q + 2)(q - 14) 32) 9(4 + z4)(2 + z2)( + z)( - z) 33) (m - 7)(n + 3)(n - 3) 34) (4 - + )(4 - - ) 3) ( )( ) 36) (2a - b)(4a2 + ab + 2b2) 37) (8s + 1)(64s2-8s + 1) 38) (p + 2z)(p - 2z)(p2 + 2pz + 4z2)(p2-2pz + 4z2) 39) -3., 3 40) -11, 3 41) -8, 9 42) - 3, ) 7, ) - 3 2, 0 4) -1, ), 4 47) 16 feet 48) 80 meters 49) 2 feet

5 Answer Ke Testname: IAREVIEW3SU06 0) a) b) ) f() = - 1 6, 7 61) 2) f() = 2, -7, ) f() = + 6 -, -1, 4) p 9 ) k 6) k - 7 7) 2 8) ) z - 2 z 60) 62) 63)

6 Answer Ke Testname: IAREVIEW3SU06 64) (0, - ); (, 0) ) (0, -2); (4, 0) ) $ ) a) C(m) = 0.3m + 27 b) $7 68) G(p) = -17,260p + 28,121 69) 8 hours, 960 miles 70) 9000 paid $12 and 30,000 paid $ 71) 7 liters of 4% solution 3. liters of % solution